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Black and White

charosh chess puzzle

By M. Charosh, from the Fairy Chess Review, 1937. White to mate in zero moves.

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Burrowed Time

In September 1924, the wheels of a truck sank into the ground behind the Pelham Courts apartments in Washington, D.C. On investigating, the building’s manager and janitor discovered a mysterious brick-lined passageway that led to a bizarre network of concrete tunnels extending as much as 32 feet underground.

The discovery put Washington into two days of wild speculation. Was this a German plot? A relic of the Civil War? But then Smithsonian Institution entomologist Harrison G. Dyar came forward to admit that he had dug the tunnels when had lived in the capital 10 years earlier. From Modern Mechanix, August 1932:


Dyar’s obsession had begun innocently enough. He told the Washington Star that in 1906 he had dug a flowerbed for his wife, and “When I was down perhaps six or seven feet, surrounded only by the damp brown walls of old Mother Earth, I was seized by an undeniable fancy to keep on going.” He had continued the project in secret for 10 years, stopping only in 1915, when he moved out of the area.

“I did it for exercise,” he told the New York Times. “Digging tunnels after work is my hobby. There’s really nothing mysterious about it.”

(Thanks, Allyson.)

Pain Puzzles

Where is pain? If my foot hurts, it’s natural to say that the pain is located in my foot, that I’m perceiving something outside my mind in the same way that I might see a rainbow or smell a rose. The same is true of itches, tickles, tingles, and other bodily sensations.

But this is troubling — suppose I discover that my foot has been amputated, and that the pain exists only in a “phantom limb.” Was I then mistaken? The pain certainly exists somewhere; it seems impossible to be wrong about that. You may convince me that the rainbow is an illusion or the rose an hallucination, but it seems absurd to suggest that one’s experience of pain is mistaken. (Inversely, pain can’t exist without someone’s feeling it. If you anesthetize me and drop a hammer on my foot, the pain isn’t somehow hidden from me — it doesn’t exist at all.)

So pain is strangely private and incorrigible — only I can know whether I’m feeling it, and I cannot be wrong about this impression. It would seem that I can have such authority only if the pain is really in my head. But “it is perfectly OK with common sense that we may have sensations in body parts other than the head — say, under our right foot! Why?” asks University of British Columbia philosopher Murat Aydede. “This, then, is another puzzle about pains and other intransitive bodily sensations: how to properly understand the common practice of locating what appear to be essentially subjective and private sensations in various parts of the body.”

In a Word

n. one who cannot read


Abraham Lincoln’s former law partner, William Henry Herndon, published a biography of the president in 1889. While gathering material for the project, he received this letter from a colleague:

Dear Herndon:

One morning, not long before Lincoln’s nomination — a year perhaps — I was in your office and heard the following: Mr. Lincoln, seated at the baize-covered table in the center of the office, listened attentively to a man who talked earnestly and in a low tone. After being thus engaged for some time Lincoln at length broke in, and I shall never forget his reply. ‘Yes,’ he said, ‘we can doubtless gain your case for you; we can set a whole neighborhood at loggerheads; we can distress a widowed mother and her six fatherless children and thereby get for you six hundred dollars to which you seem to have a legal claim, but which rightfully belongs, it appears to me, as much to the woman and her children as it does to you. You must remember that some things legally right are not morally right. We shall not take your case, but will give you a little advice for which we will charge you nothing. You seem to be a sprightly, energetic man; we would advise you to try your hand at making six hundred dollars in some other way.’



The Paradox of the Second Ace


You’re watching four statisticians play bridge. After a hand is dealt, you choose a player and ask, “Do you have at least one ace?” If she answers yes, the chance that she’s holding more than one ace is 5359/14498, which is less than 37 percent.

On a later hand, you choose a player and ask, “Do you have the ace of spades?” Strangely, if she says yes now the chance that she has more than one ace is 11686/20825, which is more than 56 percent.

Why does specifying the suit of her ace improve the odds that she’s holding more than one ace? Because, though a smaller number of potential hands contain that particular ace, a greater proportion of those hands contain a second ace. It’s counterintuitive, but it’s true.

Modern Convenience


For the stylish farmer, Jefferson Darby patented this plow attachment in 1874. The canopy can be adjusted both horizontally and vertically, “thus affording a complex and ample range of adjustment by which the shade may be shifted about as the plow changes direction and the sun moves along its course.”

“The attachment may also be attached to other agricultural implements, also upon wagons and other carriages.”

The Vision Thing


Diary entry by journalist Sydney Moseley, Aug. 1, 1928:

… I met a pale young man named Bartlett who is Secretary to the new Baird Television Company. Television! Anxious to see what it is all about … He invited me to go along to Long Acre where the new invention is installed. Now that’s something! Television!

Met John Logie Baird; a charming man — a shy, quietly spoken Scot. He could serve as a model for the schoolboy’s picture of a shock-haired, modest, dreamy, absent-minded inventor. Nevertheless shrewd. We sat and chatted. He told me he is having a bad time with the scoffers and skeptics — including the BBC and part of the technical press — who are trying to ridicule and kill his invention of television at its inception. I told him that if he would let me see what he has actually achieved — well, he would have to risk my damning it — or praising it! If I were convinced — I would battle for him. We got on well together and I have arranged to test his remarkable claim.

(Later) Saw television! Baird’s partner, a tall, good-looking but highly temperamental Irishman, Captain Oliver George Hutchinson, was nice but very nervous of chancing it with me. He was terribly anxious that I should be impressed. Liked the pair of them, especially Baird, and decided to give my support … I think we really have what is called television. And so, once more into the fray!

The Lodging-House Difficulty

A puzzle by Henry Dudeney:

dudeney lodging-house difficulty

The Dobsons secured apartments at Slocomb-on-Sea. There were six rooms on the same floor, all communicating, as shown in the diagram. The rooms they took were numbers 4, 5, and 6, all facing the sea.

But a little difficulty arose. Mr. Dobson insisted that the piano and the bookcase should change rooms. This was wily, for the Dobsons were not musical, but they wanted to prevent any one else playing the instrument.

Now, the rooms were very small and the pieces of furniture indicated were very big, so that no two of these articles could be got into any room at the same time. How was the exchange to be made with the least possible labour? Suppose, for example, you first move the wardrobe into No. 2; then you can move the bookcase to No. 5 and the piano to No. 6, and so on.

It is a fascinating puzzle, but the landlady had reasons for not appreciating it. Try to solve her difficulty in the fewest possible removals with counters on a sheet of paper.

Click for Answer

A Change of Key

5 × 55 × 555 = 152625

remains true if each digit is increased by 1:

6 × 66 × 666 = 263736